Note from [1]}, [2]}, for each connected component \((q_0,q^*_0)\)  there exists a finite word \(a_1\cdots a_n\) 
such that \(\alpha (q_0)=(a_1\cdots a_n)^\infty \in \Omega _m ^{\mathbb {N}}\)  where \(a_1\cdots a_n\)  is assumed the smallest periodic block. The right endpoint \(q^*_0\)  is the limit of sequence \(\lbrace q_\ell \rbrace \)  defined below.
Let
\(c_0^-:=a_1\cdots a_n\;\textrm {and}\; c_{\ell +1}=c_\ell \overline{c_\ell }^+, \;\;\ell =0,1,\cdots .\) 
